EP1716834A2 - Passive gravity-balanced assistive devices - Google Patents

Abstract

A passive gravity balancing device that combines the use of auxiliary parallelograms with springs to produce an orthotic device is provided for assisting movement in persons suffering from muscle weakness or impaired motor control.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS
• This application Is a continuation-in-part of US 11/113,729 and claims benefit of priority from US 11/113,729, filed April 25, 2005 , and US 60/748,429, filed December 8, 2005 , the contents of which are incorporated herein by reference.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH
• The work leading to this Invention was financed in part by the National Institute of Health (NIH) under a grant NO. 1 RO1 HD38582-01A2,
FIELD OF THE INVENTION
• This invention relates to rehabilitative assistive devices. More specifically, this invention provides a method and associated passive gravity-balanced apparatus for facilitating movement by persons suffering from muscle weakness or impaired motor control.
BACKGROUND OF THE INVENTION
• A vast number of people are affected by conditions that result in profound muscle weakness or impaired motor control. For example, people with severe muscle weakness from neurological injury, such as hemiparesis from stroke, often have substantial movement limitations, and for many people, sit-to-stand motion becomes increasingly difficult with age.
• One of the alms of rehabilitation after stroke is to improve the walking function. However, equipment available to facilitate this is severely limited. Several lower extremity rehabilitation machines have been developed recently to help retrain gait during walking. Lokornat® is an actively powered exoskeleton, designed for persons with spinal cord injury. The persons use this machine while walking on a treadmill. Mechanized Gait Trainer® (MGT) Is a single degree of freedom powered machine that drives the leg to move In a prescribed gait pattern. The machine consists of a foot plate connected to a crank and rocker system. The device simulates the phases of galt, supports the subjects according to their abilities, and controls the center of mass in the vertical and horizontal directions. Auto-Ambulator® is a rehabilitation machine for assisting individuals, with stroke and spinal cord injuries, in leg motion impairments. This machine is designed to replicate the pattern of normal galt.
• Sit-to-stand (STS) is one of the most common daily activities. It is a prerequisite for other functional movements that require ambulation and is mechanically demanding. In the United States, an estimated two million people over age 64 have difficulty in rising from a chair. Functional electrical stimulation (FES) of muscles has been used to assist disabled individuals with STS motion, in particular to assist a paraplegic person to stand from a wheelchair. Handle reactions have also been used as a measure of stimulation of leg muscles during standing up. Powered robotic assistive devices that may incorporate FES have also been designed for standing-up training. KineAssist is a robotic device for gait and balance training. It is a microprocessor controlled, motor actuated device that provides partial body weight support and postural torques on the torso.
• The use of these gait-training and sit-to-stand machines is limited in that they require external power to function, posing increased risk to the user, and require supervisory staff for safe use. Additionally, they only move persons through predetermined movement pattems rather than allowing them to move under their own control. The failure to allow persons to experience and practice appropriate movement prevents necessary changes in the nervous system to promote relearning of typical patterns. There is, therefore, a need for a rehabilitation device that provides passive assistance, supports a person according to his/her abilities and allows the person to move using his/her own muscle power.
• Gravity balancing is often used in industrial machines to decrease the required actuator efforts during motion, but has rarely been used for assistive rehabilitation devices. A machine is said to be gravity balanced if joint actuator torques are not needed to keep the system in equilibrium in any configuration. Gravity balancing is a useful principle that can assist a user in walking and in STS activity. In STS motion the required joint torques are due to gravity, passive muscle forces, and inertia. Because STS movement is relatively slow, the joint torque due to gravity is the most dominant. A gravity-balancing apparatus does not require power and keeps the human body in neutral equilibrium during the entire range of motion, reducing the amount of effort needed for the motion. A gravity-balancing apparatus may be used as a functional rehabilitative aid, a training device, or an evaluation tool for the study of specific types of motion.
SUMMARY OF THE INVENTION
• There is provided according to this Invention equipment that allows persons to use their impaired muscles to move their limbs under their own power by balancing the effects of gravity on the afflicted limbs thereby reducing the effort needed to use such limb(s). Such balancing Is achieved by transferring the weight of the afflicted limbs to a support external to the limbs, such as, for example a harness worn by the person or a supporting structure forming part of a complete training system.
• In its broader aspects the invention is a method for transferring the weight of articulated members of a system comprising a first supporting structure, and at least two interconnected articulated members pivotally attached to the support from the pivoting point to a new point on the supporting structure.
• The invention encompasses a method and an apparatus for assisting a person to move from a seated to a standing position, comprising an articulated passive gravity balanced assistive device for assisting a person to move from a first seated position to a second standing position, said person having an ankle, a calf, a thigh and a torso, the device comprising a fixed primary supporting point; a first member adapted to be attached to said calf having a first and a second end, a second member pivotally connected at one end thereof to said first member second end and adapted to be attached to said thigh, and a third member pivotally connected to another end of said second member and adapted to be attached to said torso, said members each comprising a scale length attachment point; a parallelogram structure connecting said scale length attachment points on each of said first, second and third members to a combined center of mass of said plurality of pivotally connected members and said calf, thigh and torso attached thereto, said parallelogram structure comprising first, second and third parallelograms interconnecting said scale attachment points on said first second and third members and said combined center of mass, each comprising a spring extending between opposite corners thereof, and a supporting spring extending between said center of mass and said primary supporting point; wherein said springs are selected such that the total potential energy of the articulated system is invariant with member configuration.
• There is also provided according to this invention, A method for assisting a person to move from a first seated position to a second standing position comprising transferring a weight supported on a pivoting support on a first supporting structure to a primary support, said weight comprising a weight of at least three interconnected articulated members pivotally attached to said pivoting support, each of said articulated members removably attached to said person's calf, thigh and torso respectively, the method comprising:
• I. identifying a center of mass for each of the articulated members, together with any additional weight attached to such articulated members;
• II. calculating a scale length for each of the articulated members;
• III. deriving a parallelogram structure connecting attachment points determined by said scale length on each of said first, second and third members to a combined center of mass of said plurality of pivotally connected members and said calf, thigh and torso attached thereto, said parallelogram structure comprising first, second and third parallelograms interconnecting said attachment points on said first second and third members and said combined center of mass, each comprising a spring extending between opposite corners thereof, and a supporting spring extending between said center of mass and said primary supporting point;
• IV. connecting said parallelogram structure to said three members;
• V. selecting springs to connect the combined center of mass to said primary supporting point and to said plurality of articulated members such that the total potential energy of the system is invariant with member configuration; and
• VI, connecting the combined center of mass:
  • (a) to the primary support with at least one of said selected springs; and
  • (b) to the articulated members with at least another of said selected springs,
• The invention further encompasses an apparatus for transferring the weight of at least two Interconnected articulated members from a first support to which they are pivotally attached to a second support. In addition to the interconnected articulated members, the apparatus further comprises:
• a parallelogram lever structure comprising articulated lever arms connecting the system center of mass to the articulated members at the end of a scale length measured from the point of attachment of the articulated arm:
• a primary connecting structure comprising at least one spring connecting the system center of mass to the second support; and
• at least one secondary connecting structure also comprising at least one spring, connecting the system center of mass to at least one of the articulated members.
• In a preferred embodiment, at least one spring in the primary connecting structure is a zero free length spring.
• Still according to this invention, the articulated members are designed to attach to and support the weight of human limbs such as a leg. In addition, both the pivotal attachment and the second support are located on a harness adapted to be worn by a human and the articulated members form an exoskeleton adapted for attachment to a human limb.
• Alternatively, the second attachment point may be on a fixed structure external to the harness supporting the articulated members, and the fixed structure may incorporate a treadmill or a chair.
BRIEF DESCRIPTION OF THE DRAWINGS
• Figure 1 is a three degrees of freedom planar model of the human body.
• Figure 2 is a model of the three degrees of freedom human body and device with auxiliary parallelograms to determine the center of mass of the body.
• Figure 3 is a schematic of a first embodiment of an STS device, including the placement of spring attachments for the three degrees of freedom human body.
• Figure 4 is a schematic model of a second embodiment of the STS device.
• Figures 5A and 5B show a person using the apparatus of Figure 4 in (a) sitting and (b) standing position.
• Figure 6 is a schematic representation of a training device comprising a gravity-balanced apparatus and a treadmill.
• Figures 7(a) and 7(b) show the significant elements and dimensions used in calculating the parellologram design and spring attachment points for the gravity balanced apparatus of Figure 6.
DETAILED DESCRIPTION OF THE INVENTION
• Although the invention Is Illustrated and described herein with reference to specific embodiments, the invention is not intended to be limited to the details shown. Rather, various modifications may be made in the details within the scope and range of equivalents of the claims and without departing from the invention. The figures and drawings are not to scale and only include those elements that are necessary in describing and explaining the invention. Such figures are not intended to replace complete engineering drawings.
• Gravity balancing, according to this invention, Is achieved by fixing a center of mass (COM) of combined articulated members and supported weight of the body in space using a parallelogram mechanism, and then making the total potential energy for any configuration of the articulated members of the system constant using springs. The principle involved in removing the weight of the leg, for example, is to support the weight of the leg using articulated members attached to the thigh and calf and place springs at suitable mathematically calculated positions on the articulated members such that they completely balance the effect of gravity of both the leg and members. The weight of the leg is then transferred to a support which may be a harness worn by the patient or an external structure such as a fixed support (i.e., a wall) or which may be a part of a training device such as a treadmill.
• A gravity-balanced assistive device for the human body may be designed by (i) determining the combined COM of the articulated supporting members and attached parts of the human body using auxiliary parallelograms; and (ii) selecting springs to connect the articulated members to the COM such that the total potential energy of the system Is invariant with configuration.
1. PASSIVE GRAVITY-BALANCED ASSISTIVE DEVICE FOR SIT-TO-STAND MOTION
• In one embodiment, the device is an apparatus having three degrees of freedom and utilizing straps or other convenient attachments between the corresponding moving segments of the device and the person's leg, In this embodiment, the following assumptions are made:
• (i) the motion of the body is in the sagittal plane;
• (ii) both legs have the same motion during the STS motion;
• (iii) the device links are lightweight and do not add significant mass to the moving limbs; and
• (iv) the COM of each link lies on the line connecting the two joints.
• The human body can be modeled during sit-to-stand (STS) motion as having three degrees-of-freedom (DOF) in the sagittal plane at the hip, knee, and ankle, as shown in Fig. 1. The sagittal plane approximation holds if both legs do not have any out-of-plane motion. Links I_s(00₁), I_t(0₁0₂), and I_H(0₂0₃) represent the shank (calf and ankle), thigh, and HAT (Head, Arm and Torso) segments of the human body, respectively. The head, arm and torso of the body is considered as a "HAT" body whose center of mass C_H remains fixed within itself during STS motion, C_j represents the center of mass of supporting member j, l, is the length of supporting member j, and l_cj is a distance to the center of mass of supporting member j from an origin. The origin may be a pivot point. (The subscript j stands for any of the subscripts s, t, or H, thorougout.) The angles θ_s, θ_k and θ_h are the ankle, knee and hip joint angles, respectively.
• To form parallelograms, scaled lengths d_s, d_t, and d_l, in each of the articulated members are determined. Scaled lengths d _j are determined by geometry and mass distribution. The three scaled lengths are used to form three parallelograms and associated scale length attachment points and to identify the location of the COM C (r _OC = d _s b _s+ d_t b _t+ d _H b _H) are shown in Fig. 2, where: $$d_s=\left(1/\mathrm{M}\right)\left(m_t{l}_s+m_H{l}_s+m_s{l}_{cs}\right)$$

  

  $$d_{\mathrm{t}}=\left(1/\mathrm{M}\right)\left(m_H{l}_{\mathrm{t}}+m_t{l}_{ct}\right)$$

  

  $$d_{\mathrm{H}}=\left(1/\mathrm{M}\right)m_{\mathrm{H}}{l}_{\mathrm{c}\mathrm{H}}$$

  

  
  and where: $$\mathrm{M}=m_s+m_t+m_H$$

  

m_i =

mass of a length j of the combined supporting member with attached weight,

b_j =

unit vector along member I_j and

g =

gravitational acceleration

• Having determined the COM of the system, the spring constants are next determined. Figure 3 illustrates, schematically, a first embodiment, of a STS device. The human body and the device is gravity-balanced by attaching four springs to the system, one across each of the three parallelograms and one from the COM to the fixed primary supporting point P as shown in Fig. 3. The total potential energy of the system consists of gravitational (V_g) and elastic (V_s) energies due to the springs. Its expression is given by: $$\mathrm{V}={\mathrm{V}}_{\mathrm{s}}+{\mathrm{V}}_{\mathrm{g}}=\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)\mathrm{k}{\mathrm{x}}^2+\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right){\mathrm{k}}_1{{\mathrm{x}}_1}^2+\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right){\mathrm{k}}_2{{\mathrm{x}}_2}^2+\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right){\mathrm{k}}_3{{\mathrm{x}}_3}^2-\mathrm{M}\mathrm{g}·{\mathrm{r}}_{\mathrm{o}\mathrm{c}}.$$

  

  
  Upon substitution of $${\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="imgf0002.png"\; state="\{\{state\}\}">x</figure-callout>}}^2=\Vert \mathrm{P}\mathrm{C}\Vert \cdot \Vert \mathrm{P}\mathrm{C}\Vert ,$$

  

  $${{\mathrm{x}}_1}^2=\Vert {\mathrm{O}}_1{\mathrm{S}}_1\Vert \cdot \Vert {\mathrm{O}}_1{\mathrm{S}}_1\Vert ,$$

  

  $${{\mathrm{x}}_2}^2=\Vert \mathrm{C}{\mathrm{S}}_3\Vert \cdot \Vert \mathrm{C}{\mathrm{S}}_3\Vert$$

  

  
  and $${{\mathrm{x}}_3}^2=\Vert {\mathrm{O}}_2{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="imgf0002.png"\; state="\{\{state\}\}">S</figure-callout>}}_2\Vert \cdot \Vert {\mathrm{O}}_2{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="imgf0002.png"\; state="\{\{state\}\}">S</figure-callout>}}_2\Vert$$

  

  
  and expanding the results thus obtained in terms of joint angles, one obtains: $$-\mathrm{M}\mathrm{g}·{\mathrm{r}}_{\mathrm{o}\mathrm{c}}=\mathrm{M}\mathrm{g}\left({\mathrm{d}}_{\mathrm{s}}{\mathrm{s}}_{\mathrm{a}}+{\mathrm{d}}_{\mathrm{t}}{\mathrm{s}}_{\mathrm{a}\mathrm{k}}+{\mathrm{d}}_{\mathrm{H}}{\mathrm{S}}_{\mathrm{a}\mathrm{k}\mathrm{n}}\right)$$

  

  $${\mathrm{x}}^2={\left({\mathrm{d}}_{\mathrm{s}}{\mathrm{c}}_{\mathrm{a}}+{\mathrm{d}}_{\mathrm{t}}{\mathrm{c}}_{\mathrm{a}\mathrm{k}}+{\mathrm{d}}_{\mathrm{H}}{\mathrm{c}}_{\mathrm{a}\mathrm{<figure-callout\; id="2"\; label="k\; n"\; filenames="imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}\mathrm{n}\mathrm{}}\right)}^2+{\left({\mathrm{d}}_{\mathrm{s}}{\mathrm{s}}_{\mathrm{a}}+{\mathrm{d}}_{\mathrm{t}}{\mathrm{s}}_{\mathrm{a}\mathrm{k}}+{\mathrm{d}}_{\mathrm{H}}{\mathrm{s}}_{\mathrm{a}\mathrm{k}\mathrm{n}}-\mathrm{d}\right)}^2$$

  

  $${{\mathrm{x}}_1}^2={{\mathrm{<figure-callout\; id="2"\; label="d\; t"\; filenames="imgf0002.png"\; state="\{\{state\}\}">d</figure-callout>}}_{\mathrm{t}}}^2+{\left(l_{\mathrm{s}}-{\mathrm{d}}_{\mathrm{s}}\right)}^2-2\left(l_{\mathrm{s}}-{\mathrm{d}}_{\mathrm{s}}\right)d_{\mathrm{t}}{\mathrm{c}}_{\mathrm{k}}$$

  

  $${{\mathrm{x}}_2}^2={{\mathrm{<figure-callout\; id="2"\; label="d\; H"\; filenames="imgf0002.png"\; state="\{\{state\}\}">d</figure-callout>}}_{\mathrm{H}}}^2+{\left(l_{\mathrm{s}}-{\mathrm{d}}_{\mathrm{s}}\right)}^2-2{\mathrm{d}}_{\mathrm{H}}\left(l_{\mathrm{s}}-{\mathrm{d}}_{\mathrm{s}}\right){\mathrm{c}}_{\mathrm{k}\mathrm{h}}$$

  

  $${{\mathrm{x}}_3}^2={\left(l_{\mathrm{t}}-{\mathrm{d}}_{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}}\right)}^2+{{\mathrm{<figure-callout\; id="2"\; label="d\; H"\; filenames="imgf0002.png"\; state="\{\{state\}\}">d</figure-callout>}}_{\mathrm{H}}}^2-2{\mathrm{d}}_{\mathrm{H}}\left(l_{\mathrm{t}}-{\mathrm{d}}_{\mathrm{t}}\right){\mathrm{c}}_{\mathrm{h}}.$$

  

  
  Here, c_l, s_i, c_ij, s_lj, c _ijk and s _ijk stand for cos θ_l, sin θ_l, cos (θ_i + θ _j ), sin (θ_i + θj), cos (θ_i + θ_j + θ_k) and sin (θ_i + θ_j + θ_k), respectively. Also d =||OP|| is the distance along the gravity vector between point O and the fixed primary support point P as shown in Fig. 3, and x and x_l are deformation and k and k_i are stiffness constants of the springs, where i = 1, 2, 3.. In this above analysis, it is assumed that the undeformed length of each spring is zero. In actual practice, this can achieved with a combination of a spring, cable, and pulley, as described in co-pending U.S. Patent application 11/113,729 .
• Setting next the coefficients of the configuration variables in the potential energy to zero, the desired stiffness of the springs for gravity balancing of the system are derived as: $$\mathrm{k}=\mathrm{M}\mathrm{g}/\mathrm{d}$$

  

  $${\mathrm{k}}_1=\mathrm{k}{\mathrm{d}}_{\mathrm{s}}/\left(l_{\mathrm{s}}-{\mathrm{d}}_{\mathrm{s}}\right)$$

  

  $${\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}_2=\mathrm{k}{\mathrm{d}}_{\mathrm{s}}/\left(l_{\mathrm{s}}-{\mathrm{d}}_{\mathrm{s}}\right)$$

  

  $${\mathrm{k}}_3=\mathrm{k}{\mathrm{d}}_{\mathrm{t}}/\left(l_t-{\mathrm{d}}_{\mathrm{t}}\right),$$

  
• Figure 4 shows a schematic representation of an apparatus (80) according to a second embodiment of this invention, which allows the use of springs with smaller stiffness constants The apparatus comprises two sets of articulated members 60 and 60', each set forming three parallelograms on the left and right sides, corresponding to the three parallelograms in Figure 3. The system of articulated support members serves as an exoskeleton and is mounted on a frame 64. The frame and the members may be fabricated out of a material with relatively low density and high intrinsic stiffness in order to reduce the weight of the device and provide for its easy adjustment. Exemplary materials include extruded aluminum, titanium, carbon reinforced fibers, Kevlar reinforced fibers, and reinforced glass fibers.
• The length of each articulated member may be adjusted and optimized for the user, using, for example, telescoping members. The primary springs 70 and 70' connect the centers of mass COM to the frame at the fixed primary supporting points P. The auxiliary springs within the parallelograms have been omitted for clarity; their location and points of attachment are as illustrated in Figure 3.
• The embodiment of Figure 4 allows the use of springs with reduced stiffness and also parallelograms of larger size than in the embodiment of Figure 3. This is achieved either by:
• a) attaching ankle weights 100 to shift the position of the center of mass of the shank member 110, or
• b) countering the weight of the human body using a harness 66 strapped to the torso by any appropriate means and attached to a counterweight W with a cable 120 running over pulleys 74 and 74'. The cable 120 is attached to the harness 66 at the COM of the HAT member (see Figures 2 and 3) or
• c) a combination of the two,
• As an alternative to ankle weights 100, other sources of resistance, or opposing force, may be used, such as springs.
• As a specific numerical example, if each ankle weight 100 is 3 kg and counterweight W is 23 Kg, calculated spring constants are:
• k=0.34 kN/m
• k₁=1.91 kN/m
• k₂=1.91 kN/m
• k₃=0.6kN/m
• In this embodiment, calculated required forces exerted by the springs are reduced from those of the first embodiment; by a factor of about 5 for spring k₃ up to a factor of about 12 for spring k₂.
• Figures 5a and 5b illustrate the use of an STS assist device by a human being. The device is utilized by a person by attaching articulated members 90 and 110 to the person's thigh and calf, respectively, and the harness 66 to the torso (Figure 5a), as described above. After the apparatus is attached, the user's weight is counterbalanced by the device and the user may practice standing up (Figure 5b) and sitting down (Figure 5a) a number of times to train and strengthen the required nerves and muscles.
II. PASSIVE GRAVITY-BALANCED ASSISTIVE EXERCISE AND TRAINING DEVICE
• In another embodiment of the invention, a training device comprising a two degrees of freedom apparatus and a treadmill is provided for the support of a paretic limb, i.e., a leg or a trunk, to help reduce the effect of gravity on the user's motion. This device overcomes the problem of supporting the weight of the afflicted member during a dynamic activity like walking, where the weight of the leg continuously shifts, by balancing the weight of the leg in all configurations, thereby putting the leg in, so to speak, a state of neutral equilibrium.
• The described system provides the design for an exoskeleton device for attachment to a patient's leg to assist such patient in walking. Referring to Figure 6 there is schematically illustrated a basic system according to the present invention designed for use to assist leg movement of an afflicted patient during a walking cycle on a treadmill 52. The patient 1.0, represented in the figure only partially, is In the process of lifting leg 14 while taking a stride. Leg 12 is on the ground. A harness 16 is strapped to the patient's torso. Attached to the harness is a structure 18 that includes a primary support point 20. Also attached and supported by the harness is a two member leg support system comprising articulated members 24 and 30, pivotally connected to each other at articulation 28. The two members are attached to the thigh and the calf portions of leg 14 respectively with a harness 26 and 32 (or any other attachment method) in a way that movement of the leg and articulated members is in unison. The members and attachments are strong enough to support the combined weight of the leg and articulated members.
• Preferably, the members are constructed of lightweight material such as extruded aluminum, titanium, carbon reinforced fibers, Kevlar reinforced fibers, and reinforced glass fibers. The length of the members is adjustable to conform to the length of a user's limb.
• A parallelogram formed by the members and arms 34 and 36 connects the COM 38 to points 40 and 42 on the articulated members 24 and 30. A primary spring connection 44 connects the COM to the primary support point 20. A secondary spring connection 46 connects the COM to member 24 at attachment point 29. Alternatively, spring 46 may connect the COM 38 to member 30 or to both members 24 and 30. The two spring loaded mechanisms serve to transfer the weight of the leg from pivot points 28 and 22 to support point 20.
• In Figures 7(a) and (b), line OH represents the harness, or any external structure on which the primary support point H is located. Link OA represents the length of articulated member 24 with O corresponding to the pivotal attachment 22 and A to the pivotal attachment 28. Link AB represents the member 30, where B is an end point to which is also transferred the weight of the foot of the patient. The joints or pivots usually contain bearings or similar heavy objects, which are approximated as point masses m_p1, m_p2, and m_p3. m_p3 includes the weight of the foot,
• Let:

l_i =

length of the i^th link;

l^- _i =

distance of COM of the i^th primary link from the joint of the previous link;

l^- _al =

distance of COM of the i^th auxiliary link from the joint of the previous link;

m_i=

mass of the ith primary link (mass of the leg segments Included),

m_al=

mass of the ith auxiliary link,

m_pl =

mass of the ith point mass,

û_i =

unit vector along the ith primary link,

u_l =

position vector from the point O to the center of mass of i ^th primary link,

u_al =

position vector from the point O to the center of mass of ith auxiliary link,

u_pl =

position vector from the point O to the center of mass of ith point mass,

s₁ =

distance OD,

s₂ =

distance AE

s₁ and s₂ determine the two legs of the parallelogram that identifies the COM. We will refer to s₁ and s₂ as the scale length. The scale length further identifies the point of connection of the parallelogram arms to the articulated members,
• In the preferred case where the links are made with an adjustable length, such as for example by using aluminum telescopic members, their mass remains constant, independent of their length. l^- _al is then a linear function of the length of the i^th auxiliary link.
• Let: $${l^{*}}_1={\mathrm{\alpha }}_1{l}_1$$

  

  $${\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="imgf0002.png"\; state="\{\{state\}\}">l</figure-callout>}}_2^{\ast }={\mathrm{\alpha }}_2{l}_2$$

  

  $${l^{*}}_{\mathrm{a}1}={\mathrm{\beta }}_1\left(l_1-{\mathrm{s}}_1\right)$$

  

  $${l^{*}}_{\mathrm{a}2}={\mathrm{\beta }}_2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="imgf0002.png"\; state="\{\{state\}\}">s</figure-callout>}}_2$$

  
• Where α_l and β_i are the ratios between 0 and 1. The COM is given by; $${\mathrm{R}}_{\mathrm{coin}}={\displaystyle \sum {\mathrm{m}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{i}}}/{\displaystyle \sum {\mathrm{m}}_{\mathrm{i}}}$$

  
• Where: $${\displaystyle \sum {\mathrm{m}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{i}}}={\mathrm{m}}_1{\mathrm{u}}_1+{\mathrm{m}}_2{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="imgf0002.png"\; state="\{\{state\}\}">u</figure-callout>}}_2+{\mathrm{m}}_{\mathrm{a}1}{\mathrm{u}}_{\mathrm{a}1}+{\mathrm{m}}_{\mathrm{a}2}{\mathrm{u}}_{\mathrm{a}2}+{\mathrm{m}}_{\mathrm{p}1}{\mathrm{u}}_{\mathrm{p}1}+{\mathrm{m}}_{\mathrm{p}2}{\mathrm{<figure-callout\; id="2"\; label="u\; p"\; filenames="imgf0002.png"\; state="\{\{state\}\}">u</figure-callout>}}_{\mathrm{p}}+{\mathrm{m}}_{\mathrm{p}3}{\mathrm{u}}_{\mathrm{p}3}$$

  

  $${\displaystyle \sum {\mathrm{m}}_{\mathrm{i}}}={\mathrm{m}}_1+{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="imgf0002.png"\; state="\{\{state\}\}">m</figure-callout>}}_2+{\mathrm{m}}_{\mathrm{a}1}+{\mathrm{m}}_{\mathrm{a}2}+{\mathrm{m}}_{\mathrm{p}1}+{\mathrm{m}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="imgf0002.png"\; state="\{\{state\}\}">p</figure-callout>}2}+{\mathrm{m}}_{\mathrm{p}3}$$

  
• Rewriting the vectors u _l in terms of unit vectors along the primary links û _i as follows: $${\mathrm{u}}_1=l_1^{\ast }{\widehat{\mathrm{u}}}_1;$$

  

  $${\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="imgf0002.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=l_1{\widehat{\mathrm{u}}}_1+{l^{*}}_2{\widehat{\mathrm{u}}}_2;$$

  

  $${\mathrm{u}}_{\mathrm{a}1}={\mathrm{s}}_1{\widehat{\mathrm{u}}}_1+{\mathrm{s}}_2{\widehat{\mathrm{u}}}_2+{l^{*}}_{\mathrm{a}1}{\widehat{\mathrm{u}}}_1;$$

  

  $${\mathrm{u}}_{\mathrm{a}2}={\mathrm{s}}_1{\widehat{\mathrm{u}}}_1+{l^{*}}_{\mathrm{a}2}{\widehat{\mathrm{u}}}_2;$$

  

  $${\mathrm{u}}_{\mathrm{p}1}=0;$$

  

  $${\mathrm{<figure-callout\; id="2"\; label="u\; p"\; filenames="imgf0002.png"\; state="\{\{state\}\}">u</figure-callout>}}_{\mathrm{p}}=l_2{\widehat{\mathrm{u}}}_2;$$

  

  $${\mathrm{u}}_{\mathrm{p}3}=l_1{\widehat{\mathrm{u}}}_1+l_2{\widehat{\mathrm{u}}}_2;$$

  
• Since point C is the center of mass of the entire system, u_com = s₁ û₁ + s₂ û₂ and therefore: $${\mathrm{s}}_1=l_1\left({\mathrm{m}}_{\mathrm{a}1}+{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="imgf0002.png"\; state="\{\{state\}\}">m</figure-callout>}}_2+{\mathrm{m}}_{\mathrm{p}3}+{\mathrm{m}}_{\mathrm{a}1}{\mathrm{\beta }}_1+{\mathrm{m}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="imgf0002.png"\; state="\{\{state\}\}">p</figure-callout>}2}\right)/\left({\mathrm{m}}_1+{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="imgf0002.png"\; state="\{\{state\}\}">m</figure-callout>}}_2+{\mathrm{m}}_{\mathrm{p}1}+{\mathrm{m}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="imgf0002.png"\; state="\{\{state\}\}">p</figure-callout>}2}+{\mathrm{m}}_{\mathrm{p}3}+{\mathrm{m}}_{\mathrm{a}1}{\mathrm{\beta }}_1\right)$$

  

  
  and $${\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="imgf0002.png"\; state="\{\{state\}\}">s</figure-callout>}}_2=l_2\left({\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="imgf0002.png"\; state="\{\{state\}\}">m</figure-callout>}}_2{\mathrm{<figure-callout\; id="2"\; label="\alpha "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_2+{\mathrm{m}}_{\mathrm{p}3}\right)/\left({\mathrm{m}}_1+{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="imgf0002.png"\; state="\{\{state\}\}">m</figure-callout>}}_2+{\mathrm{m}}_{\mathrm{a}2}+{\mathrm{m}}_{\mathrm{p}1}+{\mathrm{m}}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="imgf0002.png"\; state="\{\{state\}\}">p</figure-callout>}2}+{\mathrm{m}}_{\mathrm{p}3}-{\mathrm{m}}_{\mathrm{a}2}{\mathrm{<figure-callout\; id="2"\; label="\beta "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\beta </figure-callout>}}_2\right).$$

  
• Having thus obtained the COM the remaining step needed to obtain gravity balancing is to determine the springs. Balancing is achieved using springs as shown in Figure 7b. Two springs are used in this example. One end of both the springs is connected to the center of mass of the system (C In Figure 7b). The other end of spring 44 is connected to the primary support, point H in Figure 7. The second spring 46 is also connected between the COM C and member 24 of the articulated members which in the above example is connected to the thigh.
• Let x₁ and x₂ be the extended lengths of the springs with corresponding stiffness k₁ and k₂ respectively. The springs are attached to the COM making the potential energy V constant for all configurations of the articulated members. That means: $$\mathrm{V}=\left({\mathrm{k}}_1{{\mathrm{x}}_1}^2/2\right)+\left({\mathrm{k}}_2{{\mathrm{x}}_2}^2/2\right)+\mathrm{M}\mathrm{g}\mathrm{h}.$$

  

  $${{\mathrm{x}}_1}^2={\Vert \mathrm{C}\mathrm{H}\Vert }^2={\left({\mathrm{d}}_1+{\mathrm{s}}_1\cos {\mathrm{\theta }}_1+{\mathrm{s}}_2\cos \left({\mathrm{\theta }}_1-{\mathrm{<figure-callout\; id="2"\; label="\theta "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\theta </figure-callout>}}_2\right)\right)}^2+{\left({\mathrm{s}}_1\sin \mathrm{\theta }+{\mathrm{s}}_2\sin \left({\mathrm{\theta }}_1-{\mathrm{<figure-callout\; id="2"\; label="\theta "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\theta </figure-callout>}}_2\right)\right)}^2$$

  

  $${{\mathrm{x}}_2}^2={\Vert \mathrm{C}\mathrm{S}\Vert }^2={{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="imgf0002.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}^2+{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="imgf0002.png"\; state="\{\{state\}\}">s</figure-callout>}}_2}^2-2{\mathrm{d}}_2{\mathrm{s}}_2\cos {\mathrm{\theta }}_2$$

  

  
  and $$\mathrm{h}={\mathrm{d}}_1+{\mathrm{s}}_1\cos {\mathrm{\theta }}_1+{\mathrm{s}}_2\cos \left({\mathrm{\theta }}_1-{\mathrm{<figure-callout\; id="2"\; label="\theta "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\theta </figure-callout>}}_2\right)$$

  

  
  Substituting and simplifying yields V=C₀+C₁ cos θ₁+C₂ cos θ₂+C₃ cos(θ₁- θ₂),
• Where: $${\mathrm{C}}_0=\left({\mathrm{k}}_1{{\mathrm{d}}_1}^2/2\right)+\left({\mathrm{k}}_2{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="imgf0002.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}^2/2\right)+\left({\mathrm{k}}_1{{\mathrm{s}}_1}^2/2\right)+\left({\mathrm{k}}_1{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="imgf0002.png"\; state="\{\{state\}\}">s</figure-callout>}}_2}^2/2\right)+\left({\mathrm{k}}_2{{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="imgf0002.png"\; state="\{\{state\}\}">s</figure-callout>}}_2}^2/2\right)-\mathrm{M}\mathrm{g}\mathrm{d}$$

  

  $${\mathrm{C}}_1={\mathrm{k}}_1{\mathrm{s}}_1{\mathrm{d}}_1-\mathrm{M}\mathrm{<figure-callout\; id="2"\; label="g\; d\; C"\; filenames="imgf0002.png"\; state="\{\{state\}\}">g</figure-callout>}\mathrm{d}$$

  

  $${\mathrm{C}}_{}$$ $${\mathrm{}}_2={\mathrm{k}}_1{\mathrm{s}}_1{\mathrm{s}}_2-{\mathrm{k}}_2{\mathrm{d}}_2{\mathrm{s}}_2$$

  

  $${\mathrm{C}}_3={\mathrm{k}}_1{\mathrm{s}}_2{\mathrm{d}}_1-\mathrm{M}\mathrm{<figure-callout\; id="2"\; label="g\; s"\; filenames="imgf0002.png"\; state="\{\{state\}\}">g</figure-callout>}{\mathrm{s}}_{}{\mathrm{}}_2.$$

  
• All the C_i are constants if the coefficients containing trigonometric variables vanish, i.e, C₁=C₂=C₃=0, in which case the total potential energy is given by V = C₀ which is a constant. The potential energy thus becomes configuration invariant and gravity balancing is achieved. These conditions yield two independent equations: $${\mathrm{k}}_1=\mathrm{M}\mathrm{g}/{\mathrm{d}}_1\mathrm{\hspace{0.17em}}\mathrm{and}\mathrm{\hspace{0.17em}}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}_2=\mathrm{M}\mathrm{g}{\mathrm{s}}_1/{\mathrm{d}}_1{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="imgf0002.png"\; state="\{\{state\}\}">d</figure-callout>}}_2$$

  

  
  and thus provide the spring constant characteristic.
• Preferably, the springs used are zero free length springs, which means that the tension in the spring is proportional to the distance between the two connection points. If the distance between the two connection points is zero, the tension in the spring is also zero.
• Implementation of a zero free length spring was accomplished using a spring, cable and pulley as illustrated In Figure 6. To emulate the property that the distance between the connection points is zero when the force (or tension) in the spring is zero, a pulley 56 is placed on the primary support 50. A length of cable 54 + 58 is connected to the COM 38, over the pulley 56 to one end of spring 44. The other end of spring 44 is attached to a support point 20 on the primary support 50. The length of the cable 54 + 58 is chosen such that the force (or tension) in the cable (and hence the force in the simulated zero free length spring) is zero when the distance between the system center of mass COM 38 and the pulley 56 on the primary support 50 is zero.

Claims (14)

1. An apparatus comprising a plurality of pivotally connected members forming an articulated system for attaching to a person and passively assisting said person to move from a first seated position to a second standing position and vice versa by transferring the combined weight of the articulated system and said person from said person's legs to a primary support, the apparatus comprising:

   a parallelogram structure connecting a scale length attachment point on each of said plurality of pivotally connected members to a combined center of mass of said plurality of pivotally connected members;

   a first connecting spring connecting said center of mass to said primary support, and

   a second connecting spring connecting said center of mass to said plurality of pivotally connected members,

   wherein said first and second springs are selected such that the total potential energy of the articulated system is invariant with member configuration and
   wherein the articulated system comprises three degrees of freedom and is adapted for mounting on a person forming an exoskeleton having pivoting members attached to a person's torso, thigh, and calf and wherein said first supporting point is said person's ankle and said primary point is located external to said exoskeleton.
2. The apparatus according to claim 1 comprising three pivotally connected members and three parallelogram structures, each connecting a scale length attachment point on each of said pivotally connected members to said combined center of mass.
3. The apparatus according to claim 2 further comprising a third and a fourth connecting springs said second, third and fourth connecting springs connecting said center of mass, the knee joint and the hip joint to said scale length attachment point on each of said three pivotally connected members.
4. An articulated passive gravity balancing assistive device for assisting a person to move from a first seated position to a second standing position and vice versa, said person having an ankle, a calf, a thigh and a torso, the device comprising:

   a fixed primary supporting point;

   a first member adapted to be attached to said calf having a first and a second end, a second member pivotally connected at one end thereof to said first member second end and adapted to be attached to said thigh, and a third member pivotally connected to another end of said second member and adapted to be attached to said torso, said members each comprising a scale length attachment point;

   a parallelogram structure connecting said scale length attachment points on each of said first, second and third members to a combined center of mass of said plurality of pivotally connected members and said calf, thigh and torso attached thereto, said parallelogram structure comprising first, second and third parallelograms interconnecting said scale length attachment points on said first second and third members and said combined center of mass, each parallelogram comprising a spring extending between opposite corners thereof, and a supporting spring extending between said center of mass and said primary supporting point;

   wherein said springs are selected such that the total potential energy of the articulated system Is invariant with member configuration.
5. The device according to claim 4 wherein the combined center of mass is located at a distance r_oc from said first end of said first member, and wherein: $${\mathrm{r}}_{\mathrm{o}\mathrm{c}}=d_s{\mathrm{b}}_{\mathrm{s}}+d_t{\mathrm{b}}_{\mathrm{t}}+d_H{\mathrm{b}}_{\mathrm{H}}$$

   

   
   where b _j is the unit vector along member l _j and m _s , m _t and m _H are the masses of the calf, thigh and HAT (Head Arms and Torso) $$d_s=\left(1/\mathrm{M}\right)\ast \left(m_t{l}_s+m_H{l}_s+m_s{l}_{cs}\right)$$

   

   $$d_t=\left(1/\mathrm{M}\right)\ast \left(m_H{l}_t+m_t{l}_{c\mathrm{t}}\right)$$

   

   $$d_H=\left(1/\mathrm{M}\right)\ast \left(m_H{l}_{\mathrm{c}H}\right)$$

   

   
   and $$\mathrm{M}=m_s+m_t+m_H$$

   
6. The device according to claim 4 wherein said parallelogram structure comprises a first parallelogram comprising portions of said first and said second members and connecting said scale length attachment point of said first member to said scale length attachment point of said second member having one corner at said first end of said second member, and a first spring extending between said first end and an opposite corner of said first parallelogram;

   a second parallelogram comprising portions of said second and said third members and connecting said scale length attachment point of said second member to said scale length attachment point of said third member having one corner at said second end of said second member, and a second spring extending between said second end and an opposite corner of said second parallelogram;

   a third parallelogram connecting said combined center of mass of said first second and third members and said calf, thigh and torso connected thereon, said third parallelogram connecting said opposite corner of said first parallelogram, said scale length attachment point of said second member said opposite corner of said second parallelogram and said combined center of mass, said third parallelogram further comprising a third spring extending between said center of mass and said scale length attachment point on said second member; and

   a fourth spring connecting said combined center of mass to said primary supporting point.
7. The device according to claim 5 wherein said parallelogram structure comprises a first parallelogram comprising portions of said first and said second members and connecting said scale length attachment point of said first member to said scale length attachment point of said second member having one corner at said first end of said second member, and a first spring extending between said first end and an opposite corner of said first parallelogram;

   a second parallelogram comprising portions of said second and said third members and connecting said scale length attachment point of said second member to said scale length attachment point of said third member having one corner at said second end of said second member, and a second spring extending between said second end and an opposite corner of said second parallelogram;

   a third parallelogram connecting said combined center of mass of said first second and third members and said calf, thigh and torso connected thereon, said third parallelogram connecting said opposite corner of said first parallelogram, said scale length attachment point of said second member said opposite corner of said second parallelogram and said combined center of mass, said third parallelogram further comprising a third spring extending between said center of mass and said scale length attachment point on said second member; and

   a fourth spring connecting said combined center of mass to said primary supporting point.
8. The device according to claim 5 further comprising a counterweight and pulley, the counterweight exerting a force on at least one of the first, second, or third members and opposing the force exerted by at least one of the springs extending between opposite corners of the parallelograms and the supporting spring.
9. The device according to claim 5 further comprising weights attached to the first member.
10. A method for assisting a person to move from a first seated position to a second standing position comprising transferring a weight supported on a pivoting support on a first supporting structure to a primary support, said weight comprising a weight of at least three interconnected articulated members pivotally attached to said pivoting support, each of said articulated members removably attached to said person's calf, thigh and torso respectively, the method comprising:

    I. identifying a center of mass for each of the articulated members, together with any additional weight attached to such articulated members;

    II. calculating a scale length for each of the articulated members;

    III. deriving a parallelogram structure connecting attachment points determined by said scale length on each of said first, second and third members to a combined center of mass of said plurality of pivotally connected members and said calf, thigh and torso attached thereto, said parallelogram structure comprising first, second and third parallelograms interconnecting said attachment points on said first second and third members and said combined center of mass, each comprising a spring extending between opposite corners thereof, and a supporting spring extending between said center of mass and said primary supporting point;

    IV. connecting said parallelogram structure to said three members;

    V. selecting springs to connect the combined center of mass to said primary supporting point and to said plurality of articulated members such that the total potential energy of the system is Invariant with member configuration; and

    VI. connecting the combined center of mass:

    (a) to the primary support with at least one of said selected springs; and

    (b) to the articulated members with at least another of said selected springs.
11. Exercise and training apparatus for transferring a combined weight of an articulated system comprising a plurality of pivotally connected members forming a passive exoskeleton adapted for supporting at least a part of a user's body and said users limbs mounted on said exoskeleton from a first support to which said pivotally connected members are directly attached to a primary support, the apparatus comprising:

    (1) a parallelogram arm structure connecting a scale length on each of said plurality of pivotally connected members to a combined center of mass of said plurality of pivotally connected members;

    (2) a first connecting spring connecting said center of mass to said primary support, and

    (3) a second connecting spring connecting said center of mass to said plurality of pivotally connected members,

    wherein said first and second springs are selected such that the total potential energy of the articulated system is invariant with member configuration, and
    wherein the primary support comprises a treadmill apparatus adapted for use by said user.
12. Apparatus according to claim 11 wherein said articulated system pivotally connected members are each adapted to attach to and support an external weight and
    wherein the scaled length of each member is calculated to include the attached weight.
13. Apparatus according to claim 11 wherein at least one of said springs is a zero free length spring.
14. Apparatus according to claim 11 further comprising a harness supporting the exoskeleton on the user's body.

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